A superconducting (zero resistance) ring of radius \(R=2~\mbox{cm}\) and self inductance \(L=0.5~\mbox{nH}\) is located in a region of zero magnetic field. A current \(I_{0}=0.1~\mbox{A}\) circulates around the ring as shown in the figure below. What minimum work in Joules must be done on the ring to fully immerse it in a region with a uniform magnetic field \(B=0.1~\mbox{T}\) (directed into the page)?

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